Minimal Ellipsoid Circumscribing a Polytope Defined by a System of Linear Inequalities

In this paper, we will propose algorithms for calculating a minimal ellipsoid circumscribing a polytope defined by a system of linear inequalities. If we know all vertices of the polytope and its cardinality is not very large, we can solve the problem in an efficient manner by a number of existent algorithms. However, when the polytope is defined by linear inequalities, these algorithms may not work since the cardinality of vertices may be huge. Based on a fact that vertices determining an ellipsoid are only a fraction of these vertices, we propose algorithms which iteratively calculate an ellipsoid which covers a subset of vertices. Numerical experiment shows that these algorithms perform well for polytopes of dimension up to seven.     

Electrical properties and memory effect in the field effect transistor based on organic ferroelectric insulator and pentacene

We have fabricated a field effect transistor (FET) based on an organic ferroelectric insulator and molecular conductor, and investigated the electrical properties and memory effects on the PEN-FET. We have observed a drastic change in the drain current at around the coercive electric fieldE _c of the organic ferroelectric insulator in not only a FET (PEN-FET) based on a pentacene (PEN) film but also a FET (IPEN-FET) based on an iodine doped PEN film. The magnitude of the change of the drain current for the IPEN-FET is 200 times larger than that for the PEN-FET. It is expected from these results that the PEN-FET (especially the IPEN-FET) is an improvement in such devices, since it operates at a low gate electric field accompanied by the appearance of the spontaneous polarization in the organic ferroelectric insulator. In addition, we have found that the drain current for the PEN-FET does not return to the initial drain current ofE _G =0 V/cm for more than one week, even if the gate electric field is changed to 0 V/cm from 500 V/cm(>E _c ). From these results, it is suggested that the PEN-FET becomes a memory device.     

Time-resolved cavity ringdown spectroscopy on nanoparticle generation in a SiH4–H2 VHF plasma

Time-resolved cavity ringdown (τ-CRD) spectroscopy has been applied to monitor the silyl (SiH₃) radicals and nanoparticles in a pulsed very high frequency (VHF) silane-hydrogen plasma under microcrystalline silicon (μc-Si:H) deposition conditions. The measured cavity loss reveals four time intervals (I up to VI) in the first 4 s of the plasma pulse. By variation of the laser wavelength, it is demonstrated that the small cavity loss at 220 nm reflects the SiH₃ absorption in interval I. In intervals II and III, an additional cavity loss appears. This additional cavity loss corresponds to Rayleigh and Mie scattering by growing nanoparticles. Interval IV reflects the loss of nanoparticles between the electrodes during the afterglow of the plasma pulse. The evolution of the nanoparticle generation determined from the τ-CRD measurements are further confirmed by additional scanning electron microscopy analyses on the nanoparticles created in the plasma pulse.     

Influence of moisture on the viscoelastic relaxations in long aliphatic chain contained semiaromatic polyamide, (PA9‐T) fiber

The effect of moisture on the mechanical relaxation processes of semiaromatic semicrystalline polyamides synthesized by a long‐chain aliphatic diamine and terephthalic acid was investigated by dynamic viscoelastic analysis (DVA) and differential scanning calorimetry (DSC). Moreover, the implication of moisture with the amorphous and crystalline domains was also examined by temperature‐dependent wide‐angle X‐ray diffraction and Fourier transform infrared spectra. The characteristics of the relaxations such as α, β, γ, and the pronounced peak shoulder appeared at 25–100 °C in DVA tan δ curves were found to be strongly susceptible to the presence of moisture. With moisture evaporation, the peak shoulder of 25–100 °C and the β‐relaxation disappeared. The former is anticipated to originate from to the side group motion of hydrogen‐bonded water, whereas the later one is from the motions of the amide–water complex units. With the disappearance of the β‐relaxation, the γ‐relaxation appeared simultaneously in much lower temperatures and ultimately coupled with the δ‐relaxation. The γ‐relaxation is attributed to be associated with the molecular motion of the amide group and δ‐relaxation with for the motion of the methylene units. The existence of two types of water was identified in the polymer, namely, tightly bound and loosely bound. The tightly bound water is believed to be directly connected by hydrogen bonding with the strong polar groups and the loosely bound water weakly links with those connected water making hydrogen bridges. The moisture acts as a plasticizer in the polymer matrix, which causes quite a large depression in its glass transition temperature (T_g). WAXD and FTIR studies corroborated the existence of water solely in amorphous regions, i.e., no rapport of water with the crystalline parts. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2878–2891, 2003     

On global integrability of BMO functions on general domains

Extending results of Staples and Smith-Stegenga, we characterize measurable subsets of a given domainD ⊃R ⁿ on which BMO(D) functions areL ^p integrable or exponentially integrable. In particular, we characterize uniform domains by the integrability of BMO functions. We also remark on the boundedness of domains satisfying a certain integrability condition for the quasihyperbolic metric.     

Microchannel-assisted thermal-lens spectrometry for microchip analysis

We present a new method for homocysteine quantitation in human plasma based on in-capillary reaction of homocysteine with 2,2′-dipyridyl disulfide. Homocysteine is in this so-called thiol-exchange reaction quantitatively transformed in mixed disulfide concomitantly with formation of an equimolar amount of 2-thiopyridone that is further separated by micellar electrokinetic chromatography and determined specifically at 343 nm. The concentration of homocysteine is thus estimated indirectly from the result of 2-thiopyridone determination. The linear detection range for concentration versus peak area for the assay was from 0.03–3 mM (correlation coefficient 0.994) with a detection limit of 6 μM and a limit of quantitation 20 μM. The inter-day reproducibility of the peak area and the migration time were 1.37% and 0.05%, respectively. The method is simple, relatively rapid and can be easily automated. Moreover the common capillary electrophoresis apparatus with a UV detector can be used to distinguish between normal and pathological hyperhomocysteinemia plasma samples.     

Non-destructive determination of spontaneously fissioning nuclides by neutron coincidence counting using multichannel time spectroscopy

A non-destructive method for determining the amount of actinoids has been developed. The method is based on thermal neutron coincidence counting and employs a selective detection of neutrons resulting from the spontaneous fission of actinoids. The detection system is described in detail and the measurement results of²⁴⁴Cm as an example are presented. The results show that the measured fission rate of²⁴⁴Cm is consistent with the fission rate calculated from ENDF/B-V data and that the amount of²⁴⁴Cm can be determined within about 5% accuracy even in the presence of a large amount of actinoids, for example, up to 2.6·10⁶, 3.6·10⁴, or 1.6·10³ times in the mass ratio of²³⁹Pu,²⁴¹Am, or²⁴⁰Pu to²⁴⁴Cm, respectively.     

Synthesis and ion selectivity of macrocyclic metacyclophanes analogous to spherand-type calixarenes

Novel macrocyclic compounds, hexahydroxy[1.0.1.0.1.0]- (2b) and octahydroxy[1.0.1.0.1.0.1.0]metacyclophane (2c) have been prepared in 50–70% yield by base-catalyzed condensation of 5,5-di-tert-butyl-2,2-dihydroxybiphenyl (1) with formaldehyde in refluxing xylene. An attempted alkylation of the flexible macrocycles2b and2c with ethyl bromoacetate in the presence of Cs₂CO₃ under acetonitrile reflux gave only one pure stereoisomer3 and4, respectively, while other possible isomers were not observed. The structural characterization of these products is also discussed. The two-phase solvent extraction data indicated that hexaethyl ester3 and octaethyl ester4 show strong metal affinity, comparable with that of the corresponding calix[n]arenes, and a high K⁺ selectivity was observed for octaethyl ester4.¹H-NMR titration of hexaethyl ester3 and octaethyl ester4 with KSCN clearly demonstrate that a 11 complex is formed which is stable on the NMR time scale.This paper is dedicated to the commemorative issue on the 50th anniversary of calixarenes.     

Molecular Recognition Study on a Supramolecular System. Part 21. Inclusion Complexation Thermodynamics of Aliphatic Alcohols by Organoselenium Modified β-Cyclodextrins

The spectrophotometric titrations have beenperformed at 25–40 °C in aqueous solution to give the complexstability constants and the thermodynamic parametersfor the stoichiometric 1 : 1 inclusion complexation ofvarious aliphatic alcohols withmono[6-(phenylseleno)-6-deoxy]--cyclodextrin (2),mono[6-(o-, m-,p-tolylseleno)-6-deoxy]--cyclodextrin (3–5),mono[6-(p-chloro-phenyl-seleno)-6-deoxy]--cyclodextrin(6), mono[6-(benzylseleno)-6-deoxy]--cyclodextrin (7) and mono[6-(naphthaleneseleno)-6-deoxy]--cyclodextrin(8). On thebasis of the present and previous results, themolecular binding abilities and selectivities forguest aliphatic alcohols of the host -cyclodextrinderivatives (2–8) are discussed comparatively and globallyfrom the thermodynamic point of view. Thethermodynamic parameters obtained are criticalfunctions of the size/shape of aliphatic alcohols, andthe position and type of the substituent introduced tothe aromatic ring of -cyclodextrin's sidearm,which are elucidatedin terms of the conformational, electrostatic,hydrogen-bonding, and hydrophobic effects.